Questions on the IK concepts

[sketchpunk]

I've been writing an IK project for a while and I'm trying to get ik posing working correctly but its something I can never get right. Your project has a gif that shows an effect that I dont know how to replicate. When the arm moves around, the chest seems to align quite well in relation to the arm but then when the arm comes back across the body the chest seems to spring back correctly. Is that all just part of the algorithm you've written or is there maybe a second pose your using to help reset things?

Also, is there a specific order of applying IK to all the chains?

Any help in understanding how you go about doing this would be very appreciated.

Just for reference my project's repo : https://github.com/sketchpunklabs/ossos
And my current 3rd attempt at ik posing : https://twitter.com/SketchpunkLabs/status/1674445821306195969